Answer:
if interest rates fall by 2%
price of bond j will increase to $756.83, price change = $756.83 - $663.28 = $93.55 or 14.1%
price of bond k will increase to $1,317.99, price change = $1,317.99 - $1,224.47 = $93.52 or 7.64%
Explanation:
bond j coupon rate 3%, 13 years to maturity, semiannual payments, YTM 6%
bond k coupon rate 9%, 13 years to maturity, semiannual payments, YTM 6%
current market price of bond j:
YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]
0.03 = {15 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]
0.015(1,000 + market value) = 15 + [(1,000 - market value)/26]
15 + 0.015market value = 15 + 35.46 - 0.038market value
0.05346market value = 35.46
market value = 35.46 / 0.05346 = $663.28
current market price of bond k:
YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]
0.03 = {45 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]
0.015(1,000 + market value) = 45 + [(1,000 - market value)/26]
15 + 0.015market value = 15 + 65.46 - 0.038market value
0.05346market value = 65.46
market value = 65.46 / 0.05346 = $1,224.47
if YTM decrease by 2%, then:
new market price of bond j:
0.02 = {15 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]
0.01(1,000 + market value) = 15 + [(1,000 - market value)/26]
10 + 0.01market value = 15 + 35.46 - 0.038market value
0.05346market value = 40.46
market value = 40.46 / 0.05346 = $756.83
new market price of bond k:
YTM = {coupon + [(face value - market value)/n]} / [(face value + market value)/2]
0.02 = {45 + [(1,000 - market value)/26]} / [(1,000 + market value)/2]
0.01(1,000 + market value) = 45 + [(1,000 - market value)/26]
10 + 0.01market value = 15 + 65.46 - 0.038market value
0.05346market value = 70.46
market value = 70.46 / 0.05346 = $1,317.99
